Can an AI model be based on the principles of rationalism?
It depends on how you define rationality.  In the field of AI, the game theoretic conception is utilized, in sense of a rational agent.

It's important to note that a decision making agent can be perfectly rational and still be "wrong" (i.e. make sub-optimal decisions.)

This is primarily because rationality is bounded for all non-trivial problems.  The quality of decisions depends on quality of information, time and space available to make the decision in relation to the problem size, and the quality of the analytic processes. 

Logic itself has pitfalls, in that any formal system can either be complete or consistent, but never both.  

I would say that the current, strong AIs are empiricists, in that the methods are statistical, and based on testing and evaluation of results.  For instance, a Monte Carlo Tree Search (MCTS) game algorithm will play billions of games against itself and analyze the results to make the strongest choice for any given state. 

But, if one considers any decision-making agent, no matter how primitive or weak, to be a form of AI, then there can be non-empirical AI in the sense that the processes heuristic as opposed to statistical.